Jmat.Real.gamma, branch z greater than 0.5

Average Error: 60.0 → 0.6

Time: 4.9m

Precision: 64

• could not determine a ground truth for program body

  1. z = 2.6476780725355068e+101

Math

\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

↓

\[\frac{\left(\left(\left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012 + \left(\left(\left(z + 2\right) \cdot \left(\left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right) \cdot z + 676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot 771.3234287776531\right) \cdot \left(z + 3\right) + -176.6150291621406 \cdot \left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right)\right) \cdot \left(z - -5\right)\right) \cdot \left(z + 4\right) + \left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right) \cdot e^{-\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}\right)}{\left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right)\right) \cdot \left(z + 4\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z}\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right) \cdot e^{-\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}\right)\]

C

double f(double z) {
        double r37538169 = atan2(1.0, 0.0);
        double r37538170 = 2.0;
        double r37538171 = r37538169 * r37538170;
        double r37538172 = sqrt(r37538171);
        double r37538173 = z;
        double r37538174 = 1.0;
        double r37538175 = r37538173 - r37538174;
        double r37538176 = 7.0;
        double r37538177 = r37538175 + r37538176;
        double r37538178 = 0.5;
        double r37538179 = r37538177 + r37538178;
        double r37538180 = r37538175 + r37538178;
        double r37538181 = pow(r37538179, r37538180);
        double r37538182 = r37538172 * r37538181;
        double r37538183 = -r37538179;
        double r37538184 = exp(r37538183);
        double r37538185 = r37538182 * r37538184;
        double r37538186 = 0.9999999999998099;
        double r37538187 = 676.5203681218851;
        double r37538188 = r37538175 + r37538174;
        double r37538189 = r37538187 / r37538188;
        double r37538190 = r37538186 + r37538189;
        double r37538191 = -1259.1392167224028;
        double r37538192 = r37538175 + r37538170;
        double r37538193 = r37538191 / r37538192;
        double r37538194 = r37538190 + r37538193;
        double r37538195 = 771.3234287776531;
        double r37538196 = 3.0;
        double r37538197 = r37538175 + r37538196;
        double r37538198 = r37538195 / r37538197;
        double r37538199 = r37538194 + r37538198;
        double r37538200 = -176.6150291621406;
        double r37538201 = 4.0;
        double r37538202 = r37538175 + r37538201;
        double r37538203 = r37538200 / r37538202;
        double r37538204 = r37538199 + r37538203;
        double r37538205 = 12.507343278686905;
        double r37538206 = 5.0;
        double r37538207 = r37538175 + r37538206;
        double r37538208 = r37538205 / r37538207;
        double r37538209 = r37538204 + r37538208;
        double r37538210 = -0.13857109526572012;
        double r37538211 = 6.0;
        double r37538212 = r37538175 + r37538211;
        double r37538213 = r37538210 / r37538212;
        double r37538214 = r37538209 + r37538213;
        double r37538215 = 9.984369578019572e-06;
        double r37538216 = r37538215 / r37538177;
        double r37538217 = r37538214 + r37538216;
        double r37538218 = 1.5056327351493116e-07;
        double r37538219 = 8.0;
        double r37538220 = r37538175 + r37538219;
        double r37538221 = r37538218 / r37538220;
        double r37538222 = r37538217 + r37538221;
        double r37538223 = r37538185 * r37538222;
        return r37538223;
}

↓

double f(double z) {
        double r37538224 = z;
        double r37538225 = 0.9999999999998099;
        double r37538226 = r37538225 * r37538225;
        double r37538227 = -1259.1392167224028;
        double r37538228 = -1.0;
        double r37538229 = r37538224 - r37538228;
        double r37538230 = r37538227 / r37538229;
        double r37538231 = r37538230 * r37538230;
        double r37538232 = r37538225 * r37538230;
        double r37538233 = r37538231 - r37538232;
        double r37538234 = r37538226 + r37538233;
        double r37538235 = r37538224 * r37538234;
        double r37538236 = 2.0;
        double r37538237 = r37538224 + r37538236;
        double r37538238 = r37538235 * r37538237;
        double r37538239 = 3.0;
        double r37538240 = r37538224 + r37538239;
        double r37538241 = r37538238 * r37538240;
        double r37538242 = -0.13857109526572012;
        double r37538243 = r37538241 * r37538242;
        double r37538244 = pow(r37538225, r37538239);
        double r37538245 = pow(r37538230, r37538239);
        double r37538246 = r37538244 + r37538245;
        double r37538247 = r37538246 * r37538224;
        double r37538248 = 676.5203681218851;
        double r37538249 = r37538248 * r37538234;
        double r37538250 = r37538247 + r37538249;
        double r37538251 = r37538237 * r37538250;
        double r37538252 = 771.3234287776531;
        double r37538253 = r37538235 * r37538252;
        double r37538254 = r37538251 + r37538253;
        double r37538255 = r37538254 * r37538240;
        double r37538256 = -176.6150291621406;
        double r37538257 = r37538256 * r37538238;
        double r37538258 = r37538255 + r37538257;
        double r37538259 = -5.0;
        double r37538260 = r37538224 - r37538259;
        double r37538261 = r37538258 * r37538260;
        double r37538262 = r37538243 + r37538261;
        double r37538263 = 4.0;
        double r37538264 = r37538224 + r37538263;
        double r37538265 = r37538262 * r37538264;
        double r37538266 = r37538260 * r37538241;
        double r37538267 = 12.507343278686905;
        double r37538268 = r37538266 * r37538267;
        double r37538269 = r37538265 + r37538268;
        double r37538270 = atan2(1.0, 0.0);
        double r37538271 = r37538270 * r37538236;
        double r37538272 = sqrt(r37538271);
        double r37538273 = 0.5;
        double r37538274 = 7.0;
        double r37538275 = 1.0;
        double r37538276 = r37538224 - r37538275;
        double r37538277 = r37538274 + r37538276;
        double r37538278 = r37538273 + r37538277;
        double r37538279 = r37538273 + r37538276;
        double r37538280 = pow(r37538278, r37538279);
        double r37538281 = r37538272 * r37538280;
        double r37538282 = -r37538278;
        double r37538283 = exp(r37538282);
        double r37538284 = r37538281 * r37538283;
        double r37538285 = r37538269 * r37538284;
        double r37538286 = r37538266 * r37538264;
        double r37538287 = r37538285 / r37538286;
        double r37538288 = 9.984369578019572e-06;
        double r37538289 = r37538288 / r37538277;
        double r37538290 = 1.5056327351493116e-07;
        double r37538291 = r37538274 + r37538224;
        double r37538292 = r37538290 / r37538291;
        double r37538293 = r37538289 + r37538292;
        double r37538294 = r37538293 * r37538284;
        double r37538295 = r37538287 + r37538294;
        return r37538295;
}

Error

Bits error versus z

Derivation

1. Initial program 60.0

   \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

2. Simplified 0.8

   \[\leadsto \color{blue}{\left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)}\]
3. Using strategy rm

4. Applied flip3-+ 0.8

   \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \color{blue}{\frac{{0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}}{0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)}}\right)\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

5. Applied frac-add 1.0

   \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \color{blue}{\frac{676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)}{z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)}}\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

6. Applied frac-add 1.0

   \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\left(\color{blue}{\frac{771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)}{\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)}} + \frac{-176.6150291621406}{z + 3}\right) + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

7. Applied frac-add 0.9

   \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \left(\color{blue}{\frac{\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406}{\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)}} + \frac{-0.13857109526572012}{z - -5}\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

8. Applied frac-add 1.0

   \[\leadsto \left(\frac{12.507343278686905}{z + 4} + \color{blue}{\frac{\left(\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406\right) \cdot \left(z - -5\right) + \left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012}{\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)}}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

9. Applied frac-add 1.0

   \[\leadsto \color{blue}{\frac{12.507343278686905 \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right) + \left(z + 4\right) \cdot \left(\left(\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406\right) \cdot \left(z - -5\right) + \left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012\right)}{\left(z + 4\right) \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right)}} \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

10. Applied associate-*l/ 0.6

    \[\leadsto \color{blue}{\frac{\left(12.507343278686905 \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right) + \left(z + 4\right) \cdot \left(\left(\left(771.3234287776531 \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z + 2\right) \cdot \left(676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right) + z \cdot \left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right)\right)\right) \cdot \left(z + 3\right) + \left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot -176.6150291621406\right) \cdot \left(z - -5\right) + \left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012\right)\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)}{\left(z + 4\right) \cdot \left(\left(\left(\left(z + 2\right) \cdot \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right)\right) \cdot \left(z + 3\right)\right) \cdot \left(z - -5\right)\right)}} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) \cdot \left(\left({\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot e^{-\left(\left(7 + \left(z - 1\right)\right) + 0.5\right)}\right)\]

11. Final simplification 0.6

    \[\leadsto \frac{\left(\left(\left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right) \cdot -0.13857109526572012 + \left(\left(\left(z + 2\right) \cdot \left(\left({0.9999999999998099}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}\right) \cdot z + 676.5203681218851 \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) + \left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot 771.3234287776531\right) \cdot \left(z + 3\right) + -176.6150291621406 \cdot \left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right)\right) \cdot \left(z - -5\right)\right) \cdot \left(z + 4\right) + \left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right) \cdot e^{-\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}\right)}{\left(\left(z - -5\right) \cdot \left(\left(\left(z \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - 0.9999999999998099 \cdot \frac{-1259.1392167224028}{z - -1}\right)\right)\right) \cdot \left(z + 2\right)\right) \cdot \left(z + 3\right)\right)\right) \cdot \left(z + 4\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(z - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z}\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right) \cdot e^{-\left(0.5 + \left(7 + \left(z - 1\right)\right)\right)}\right)\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))